Divisibility Rule of 4

The divisibility rule of 4 states that a given number is divisible by 4 if the last two digits of the number are zeros, or they form a number that is divisible by 4. It is also known as the divisibility test of 4. The divisibility rule of 4 helps to find out whether a number is divided by 4 or not without performing the division. The first four whole numbers that are divisible by 4 are 0, 4, 8, 12, and 16. All these are the multiples of 4 and every multiple of 4 is completely divisible by 4.

According to the divisibility rule of 4, a whole number is said to be divisible by 4 if it has fulfilled one of the two conditions:

• If the last two digits of the given number are zeros. This means the number has zeros at tens place and ones place. For example, in 300 the last two digits are 00, therefore, 300 is divisible by 4.
• If the last two digits of the given number form a number that is exactly divisible by 4. For example, in 316, the last two digits form the number 16 which is divisible by 4. Therefore, 316 is divisible by 4.

Divisibility Rule of 4 with Examples

The divisibility rule of 4 can be understood with the help of the following examples.

Example: Test the divisibility of the following numbers by 4.

a.) 1124

b.) 1171

c.) 1300

d.) 500

Solution:

a.) In 1124, the last two digits in the given number form a number 24 which is divisible by 4 (24 ÷ 4 = 6)
Thus, 1124 is divisible by 4. This can be verified as follows: 1124 ÷ 4 = 281

b.) In 1171, the last two digits in the given number form a number 71 which is not completely divisible by 4 (71÷ 4 = 17 is the quotient and 3 is the remainder)
Thus, 1171 is not divisible by 4.

c.) In 1300, the last two digits in the given number are zeros. That means 1300 is completely divisible by 4.
1300 ÷ 4 = 325
Thus, 1300 is divisible by 4.

d) In 500, the last two digits in the given number are zeros. That means 500 is completely divisible by 4.
500 ÷ 4 = 125
Thus, 500 is divisible by 4.

Divisibility rules help in solving problems without the process of division.

The divisibility rule of 4 states that if the number has two zeros in the end or the last two digits form a number that is exactly divided by 4, then the given number is also divisible by 4. Therefore, for any large numbers, we check the last two digits and apply the divisibility rule of 4 and can find out whether the large number is divisible by 4 or not.

Example 1: in 238900 the last two digits at tens place and ones place are zeros. That means 238900 is divisible by 4.
238900 ÷ 4 = 59725
Thus, 238900 is divisible by 4.

Example 2: In 148936 the last two digits at tens place and ones place form a number 36 which is divisible by 4 (36 ÷ 4 = 9).
148936 ÷ 4 = 37234
Thus, 148936 is divisible by 4.

The divisibility rules of 4 and 6 are completely different. In the divisibility rule of 4, if the last two digits are zeros or the number formed by the last two digits is exactly divisible by 4, then we can say that a number is divisible by 4. However, according to the divisibility rule of 6, a number is said to be divisible by 6 only if the number is divisible by both 2 and 3. In the divisibility test of 4, we check the last two digits, and in the divisibility test of 6, we check whether the whole number is divisible by 2 and 3 or not. For example, let us check if 936 is divisible by 6. Since the last digit of 936 is an even number, it can be said that 936 is divisible by 2. Now, let us check its divisibility by 3. The sum of the digits is 9 + 3 + 6 = 18, which is divisible by 3. This means 936 is divisible by 3 as well. Therefore, it can be said that the number 936 is completely divisible by 6.

The divisibility test of 4 and 8 are slightly similar. In the divisibility test of 4, we check the last two digits, if the last two digits are zeros or the number formed by the last two digits of a number is exactly divisible by 4 then the original number is also divisible by 4. In the divisibility test of 8, we check the last three digits, if the last three digits are zeros or the number formed by the last three digits of a number is exactly divisible by 8 then the original number is also divisible by 8. For example, let us check if 61816 is divisible by 8. If we check the last 3 digits they form a number 816 which is divisible by 8. Therefore, it can be said that 61816 is divisible by 8.

☛ Related Topics

• Divisibility Rule of 3
• Divisibility Rule of 5
• Divisibility Rule of 6
• Divisibility Rule of 7
• Divisibility Rule of 8
• Divisibility Rule of 9
• Divisibility Rule of 11
• Divisibility Rule of 13

What is the Divisibility Rule of 4?

The divisibility rule of 4 tells that a number is said to be divisible by 4 if the last two digits of the number are zeros or they form a number that is divisible by 4. For example, 2300 is divisible by 4 because there are two zeros in the end of the number. Similarly, 488 is also divisible by 4 because the last two digits 88 are divisible by 4.

Using the Divisibility Rule of 4, Check if 14540 is Divisible by 4.

First, we need to check that the number formed by the last two digits of a given number is divisible by 4 or not. In the given number 14540, the number formed by the last two digits is 40, and 40 is divisible by 4. Thus, 14540 is divisible by 4.

What is the Divisibility Rule of 4 and 8?

The divisibility rule of 4 and 8 are slightly similar. In the divisibility rule of 4, we focus on the last two digits of the number. If the last two digits are zeros or the number formed by the last two digits of a number is exactly divisible by 4 then we can say that the given number is also divisible by 4. For example, 800, 900, and 348 are all divisible by 4 as they fulfill the condition of the divisibility rule of 4.

In the divisibility rule of 8, we focus on the last three digits of the number. If the last three digits are zeros or the number formed by the last three digits of a number is exactly divisible by 8 then we can say that the original number is also divisible by 8. For example, 8000, 9000, and 3896 are all divisible by 8 as they fulfill the condition of the divisibility rule of 8.

How do you know if a Big Number is Divisible by 4?

According to the divisibility rule of 4, any big number is exactly divided by 4 if the number formed by the digits at tens and ones place is exactly divisible by 4. For example, the number 2,146,484 is exactly divisible by 4 because the number 84 (last two digits) is divisible by 4.

Using the Divisibility Rule of 4, Check if 19500 is Divisible by 4.

Yes, 19500 is divisible by 4 because according to the divisibility test of 4 if the number has two zeros in the end or the last two digits form a number that is exactly divided by 4 then the number is also divisible by 4.

What Numbers are Divisible by 4?

According to the divisibility rule of 4, if the last two digits of the given number are zeros or they form a number that is completely divisible by 4, then the given number is said to be divisible by 4. For example, 412, 532, 700 and so on are a few numbers that are divisible by 4 because they fulfill the divisibility test of 4.